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You'll be able to complete this marathon - you just won't be able to complete it fast.

The key for you right now is to start getting comfortable with running longer distances. You didn't mention what pace you typically run at, so I'm going to assume it's 8mph for the sake of calculations (you can adjust depending on what it actually is). If you feel good after those 5-6 mile runs, take this first week and try to increase those runs to 7-8 miles, and see how that goes. Once you find a point where you're very tired after the run (or now, if you're very tired after 5-6 miles), drop your pace to 6mph and try to add on 3-4 miles. This pace should feel very easy at the beginning - you'll likely want to bring it up. It's critical that you gain a feeling for how to not bring it up and to keep it consistent.

You should feel good at the end of your longer, slower run; if you don't, try to slow the pace even further. Once you've found a comfortable speed where you can do ~10 miles (aim to find this by week 3), start adding on a mile to each weekend run. You can keep the odd run shorter, as this will help the slow runs to feel easier. If the runs ever feel exceedingly difficult, drop the pace a little bit. Assuming you start adding on the miles week 3, you'll be right at 24 miles in the 10th week. However, once you hit 20 miles, I'd recommend remaining at that distance, and instead trying to bring the pace back up somewhat and go for 10-12 mile runs.

By the end of 10 weeks, you'll have a far better understanding of the limitations of your body, and will know what pace to attack the 24 mile run at. You'll have to avoid the desire to increase the pace on raceday - while the adrenaline will help, it's not going to be enough for a huge speed increase. If you stick with it, you should be able to complete the final run at a few mph slower than your current 5 mile pace.